In a town, the population was 9000. In 1 year, the male population increased by 10% and the female population increased by 8%, but the total population increased by 9%. The increased female population in the town is:

Given:

Initial total population = 9000

Increase in male population = 10%

Increase in female population = 8%

Increase in total population = 9%

Formula Used:

Increase in population = (Percentage increase / 100) × Initial population

Let the initial male population be M and the initial female population be F.

M + F = Initial total population

Calculation:

Initial total population = 9000

Let the initial male population be M.

Let the initial female population be F.

M + F = 9000 (Equation 1)

Increase in male population = 10% of M = 0.10M

New male population = M + 0.10M = 1.10M

Increase in female population = 8% of F = 0.08F

New female population = F + 0.08F = 1.08F

Increase in total population = 9% of 9000 = (9 / 100) × 9000 = 0.09 × 9000 = 810

New total population = 9000 + 810 = 9810

Also, New total population = New male population + New female population

9810 = 1.10M + 1.08F (Equation 2)

From Equation 1, M = 9000 - F. Substitute this into Equation 2:

9810 = 1.10(9000 - F) + 1.08F

9810 = 9900 - 1.10F + 1.08F

0.02F = 9900 - 9810

F = 90 / 0.02 = 4500

Initial female population (F) = 4500

Increased female population = 1.08F = 1.08 × 4500

Increased female population = 4860

The increased female population in the town is 4860.